MiJceUanea Curiofa. 1 55 



C O R O L 



If m be expounded by any Term of the 

 following Series, o, 2, 4, <5, 8, &c the Qua- 

 drature of the Curve, whole Ordinate is 



x m 



— , depends upon the Reftification of 



rr~\-xx 



the Arch of a Circle. For defcribing the 

 Circle AEG on the Center C, with the Ra- 

 dius CA=r, draw the Tangent AK=x, and 

 join CK meeting the Periphery in E 7 then 

 the Arch AE divided by rr is equal to the 



x° 



Area of the Curve, whofe Ordinate is . 



rr-\~xx 



General Corollaries to tbefe fix Theorems. 



EVery Mechanick Curve (whofe Quadra- 

 ture depends upon any one of that In- 

 finite Number of Curves, whofe Ordinate? 



/' 



have the following Forms, x y dx~Vxx^ 

 : x m x m 



x V rr'Yxx^ x V rr+xx, d'Yx 



\Idx ± 



X m v 



■ - J may be fquar'd by thefe Series. It 



rr-\-xx' 



may fuffice to illuftrate this by an Exam-' 

 pie, 



Sup- 



